Project 10: Quantum Error Mitigation (Zero Noise Extrapolation)

Build a noise model and apply zero-noise extrapolation to improve results.

Project Overview

Attribute Value
Difficulty Level 3: Advanced
Time Estimate 1-2 weeks
Main Language Python
Alternative Languages Julia, C++
Knowledge Area Noise modeling
Tools Qiskit noise models
Main Book “Quantum Computation and Quantum Information” by Nielsen & Chuang

What you’ll build: A demo that adds noise to circuits, runs them at multiple noise levels, and extrapolates back to zero.

Why it teaches quantum: Real quantum hardware is noisy. Mitigation is essential for practical use.

Core challenges you’ll face:

  • Defining noise models
  • Scaling noise levels systematically
  • Fitting extrapolation curves

Real World Outcome

You will show improved expectation values after extrapolation compared to raw noisy results.

Example Output:

$ python zne.py --circuit bell
Raw expectation: 0.72
Extrapolated: 0.94

Verification steps:

  • Compare to ideal simulator output
  • Plot expectation vs noise level

The Core Question You’re Answering

“How can we reduce noise effects without full error correction?”

Error mitigation is the near-term answer to noisy devices.

Concepts You Must Understand First

Stop and research these before coding:

  1. Noise channels
    • What are depolarizing and dephasing channels?
    • Book Reference: Nielsen & Chuang, Ch. 8
  2. Zero-noise extrapolation
    • Why does scaling noise allow extrapolation?
    • Book Reference: “Quantum Error Mitigation” by Temme et al.
  3. Expectation values
    • How do you measure observables under noise?
    • Book Reference: Nielsen & Chuang, Ch. 2

Questions to Guide Your Design

  1. Noise scaling
    • How will you scale noise (gate folding, repetition)?
    • How many noise levels will you sample?
  2. Fitting method
    • Will you use linear or exponential fits?
    • How will you evaluate fit quality?

Thinking Exercise

Extrapolation Intuition

If expectation values are 0.8 at noise level 1 and 0.6 at noise level 2, what would a linear extrapolation predict at noise 0?

Questions while working:

  • Why might linear fits fail?
  • How does circuit depth affect noise scaling?

The Interview Questions They’ll Ask

Prepare to answer these:

  1. “What is error mitigation vs error correction?”
  2. “What is zero-noise extrapolation?”
  3. “How do you scale noise in a circuit?”
  4. “Why does noise reduce expectation values?”
  5. “What are the limits of mitigation?”

Hints in Layers

Hint 1: Starting Point Start with a simple circuit and known expectation.

Hint 2: Next Level Add depolarizing noise at different strengths.

Hint 3: Technical Details Fit a curve to expectation vs noise and extrapolate.

Hint 4: Tools/Debugging Compare to ideal simulator results to confirm improvement.

Books That Will Help

Topic Book Chapter
Noise channels Nielsen & Chuang Ch. 8
ZNE “Quantum Error Mitigation” by Temme et al. Section 3
Expectation values Nielsen & Chuang Ch. 2

Implementation Hints

  • Keep circuits small to reduce runtime.
  • Use multiple seeds to average noise effects.
  • Plot results to validate extrapolation.

Learning Milestones

  1. First milestone: You can build a noise model and measure effects.
  2. Second milestone: You can apply zero-noise extrapolation.
  3. Final milestone: You can explain mitigation tradeoffs.